U.S. patent number 6,138,103 [Application Number 09/362,010] was granted by the patent office on 2000-10-24 for method for production planning in an uncertain demand environment.
This patent grant is currently assigned to International Business Machines Corporation. Invention is credited to Feng Cheng, Daniel Patrick Connors, Thomas Robert Ervolina, Ramesh Srinivasan.
United States Patent |
6,138,103 |
Cheng , et al. |
October 24, 2000 |
Method for production planning in an uncertain demand
environment
Abstract
A decision-making method suitable for production planning in an
uncertain demand environment. To this end, the method comprises
combining an implosion technology with a scenario-based analysis,
thus manifesting, a sui generis capability which preserves the
advantages and benefits of each of its subsumed aspects.
Inventors: |
Cheng; Feng (Elmsford, NY),
Connors; Daniel Patrick (Wappingers Falls, NY), Ervolina;
Thomas Robert (Hopewell Junction, NY), Srinivasan;
Ramesh (San Jose, CA) |
Assignee: |
International Business Machines
Corporation (Armonk, NY)
|
Family
ID: |
25218947 |
Appl.
No.: |
09/362,010 |
Filed: |
July 27, 1999 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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815825 |
Mar 12, 1997 |
6006192 |
|
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Current U.S.
Class: |
705/7.37;
700/103; 705/19 |
Current CPC
Class: |
G06Q
10/04 (20130101); G06Q 10/06375 (20130101); G06Q
10/06393 (20130101); G06Q 10/087 (20130101); G06Q
40/00 (20130101); G06Q 20/201 (20130101); G06Q
20/207 (20130101); G06Q 30/0202 (20130101); G06Q
10/0875 (20130101) |
Current International
Class: |
G06Q
10/00 (20060101); G06F 017/60 (); G06F 015/21 ();
G06F 015/60 () |
Field of
Search: |
;705/7,8,9,10,29,28,20,35,14 ;700/106,103 |
Other References
Zapel, Gunter; "Production planning in the case of uncertain
demand. Extension for an MRP II concept"; Int'l. Journal of
Production Economics; vol. 46-47, p. 153-64, Dec. 1, 1996..
|
Primary Examiner: MacDonald; Allen R.
Assistant Examiner: Kanof; Pedro R.
Attorney, Agent or Firm: Scully, Scott, Murphy & Presser
Kaufman, Esq.; Stephen C.
Parent Case Text
CROSS REFERENCE TO RELATED APPLICATION
The present application is a continuation of application Ser. No.
08/815,825, filed Mar. 12, 1997 now U.S. Pat. No. 6,006,192.
Claims
What is claimed:
1. A program storage readable by a machine, tangibly embodying a
program of instructions executable by a machine to perform method
steps for production planning in an uncertain demand environment,
said method steps comprising:
a) inputting a plurality of demand scenarios over a timing horizon
and a probability associated with each of said demand scenario
which represent uncertainties in a demand environment;
b) employing a scenario-based analysis including the steps of
performing multiple optimization runs against different demand
scenarios;
c) combining an implosion technology with the scenario-based
analysis for generating for any one individual demand scenario, a
deterministic solution which is optimal for the particular demand
scenario; and,
d) generating an output comprising a payoff table that includes
said solution for each demand scenario, each said solution being
optimized in accordance with a selected performance measure.
2. A device according to claim 1, wherein the method comprises
creating a production plan based initially on a particular demand
scenario.
3. A device according to claim 2, wherein the method comprises a
step of adjusting the production plan according to unfolding sequel
demand scenarios.
4. A device according to claim 2, wherein the method comprises
obtaining from the production plan an implementable production
policy for an entire demand scenario tree.
5. A device according to claim 1, wherein the method comprises
computing an expected performance measure for each implementable
production policy based on a particular initial demand
scenario.
6. The program storage readable by a machine as claimed in claim 1,
wherein said selected performance measure includes revenue.
7. The program storage readable by a machine as claimed in claim 1,
wherein said selected performance measure includes profit, said
payoff table providing solutions that take into account costs
including one of backlog penalties and obsolescence.
8. The program storage readable by a machine as claimed in claim 1,
wherein said selected performance measure includes serviceability.
Description
FIELD OF THE INVENTION
This invention relates to a decision-making method suitable for
production planning in an uncertain demand environment.
INTRODUCTION TO THE INVENTION
One of the important issues in production planning is to deal with
uncertainties associated with demand. While a vast volume of the
literature addresses this issue, production/materials planning
under uncertainty still presents a significant challenge to
researchers and practitioners.
There have been many interesting studies in inventory/production
planning theory. However, we have discerned that the results
obtained so far are either based on over-simplified assumptions, or
are computationally intractable for real-world problems.
For example, the well-known EOQ (Economic Order Quantity) model
invented in the early part of this century is considered to be one
of the earliest and most important developments in the mathematical
inventory/production planning theory. The basic EOQ model still
remains the most widely used analytical method for inventory
control in practice. In the 50's and 60's, more serious
mathematical analyses of various inventory problems were undertaken
and became the fundamentals of later developments in the area.
The solutions available in the literature can be categorized into
two general types. One type of solution can be considered to be the
extensions of the EOQ model where a simple form solution can be
obtained under certain assumptions about demand, costs, and other
parameters. Especially, the studies on single product and single
location problems have produced a rich collection of analytical
models, including many variations of the EOQ model and (s,S)
models. This type of solution is usually easy to implement and
interpret because of its simplicity. However, the assumptions made
to ensure the validity of the solution are often restrictive and
may not be consistent with the reality. Another general type of
solution normally involves a mathematical programming formulation,
which allows more flexible modeling of the underlying
production/inventory process, and, therefore, can handle a wide
range of real-world applications. A major limitation to the use of
math programming solutions is often the large size of real-world
problems, even though the advances over the years of computer
hardware and software have greatly enhanced our ability to solve
large scale math programming problems .
In the last two decades, material requirements planning (MRP) has
become a common practice in industry for the purposes of production
planning and control. The earlier versions of MRP largely focused
on managing materials. The same concepts were applied to labor,
another important factor in planning. Beyond labor and material,
further applications dealt with equipment, tooling and other
resources. These variations gave rise to the broader term,
manufacturing resource planning, which is often referred to as MRP
II.
As a particular example, we note the implosion(TM) technology
developed in IBM which is able to provide feasible and optimal
production plans under materials and capacity constraints.
Traditional MRP systems perform requirements analysis by using
demands and the Bill Of Materials (BOM) to determine the necessary
resources to fulfill the demand. In contrast, implosion(TM)-based
systems can perform resource allocation under constraints by using
demands, available resources, and the Bill Of Manufacture (includes
BOM as well as Bill of Capacities) to determine a feasible product
mix which meets the user goals. These goals correspond to user
defined criteria such as customer serviceability, profit
maximization, inventory minimization, and revenue maximization.
However, the effectiveness of MRP-based systems may be limited by
the weaknesses of the basic MRP framework. Particularly,
uncertainty is ignored in the standard MRP approach. All
parameters, such as the future demand, production rates, yields,
lead times, etc., are treated as if they were known with
certainty.
One useful technique often used to deal with the uncertainty is the
scenario-based analysis. Scenarios are usually used as a simplified
way of representing the uncertainty. By performing multiple
optimization runs against different scenarios, one can gain the
insights needed to plan effectively for an uncertain future.
Escudero and Kamesam (1992) provide a scenario-based solution
methodology for solving aggregate production planning problems
under demand uncertainty. They obtain an implementable policy by
solving a stochastic LP problem. (See Escudero, L. and P. Kamersom,
MRP Modeling via Scenarios, Research Report, RC-17982.)
SUMMARY OF THE INVENTION
We have now discovered a "Payoff Table" approach that is designed
as a decision-making methodology for production planning in an
uncertain demand environment. The methodology comprises combining
the power of the scenario-based analysis and the implosion
technology. For each individual demand scenario, the implosion
method may be used to provide a deterministic solution which is
optimal given the particular demand scenario. Furthermore, we also
compute the performance measure of each solution against all other
potential demand scenarios. The complete enumeration of performance
measures for each solution against all demand scenarios produces a
payoff table, which may be referred to as a production plan payoff
table (PPPT).
Accordingly, we disclose a novel program storage device readable by
a machine, tangibly embodying a program of instructions executable
by the machine to perform method steps for production planning in
an uncertain demand environment, said method steps comprising:
1) representing the uncertainty in the demand environment by
employing a scenario-based analysis including the steps of
performing multiple optimization runs against different demand
scenarios;
and
2) combining an implosion technology with the scenario-based
analysis for generating for any one individual demand scenario, a
deterministic solution which is optimal for the particular demand
scenario.
The novel method as defined can realize important advantages, as
enumerated below. Here, it is significant to note that the method,
by way of its agency of combining implosion technology with a
scenario-based analysis, can perserve the benefits of each
disparate aspect, while manifesting in combination a sui generis
capability of qualitative advantage and utility over the prior
art.
BRIEF DESCRIPTION OF THE DRAWING
The invention is illustrated in the accompanying drawing, in
which:
FIG. 1 shows a canonical scenario tree;
FIG. 2 shows a general scenario tree;
and
FIGS. 3-8 show illustrative output computer display windows
generated in accordance with the present invention.
DETAILED DESCRIPTION OF THE INVENTION
The detailed description of the invention is organized as follows.
In Section 1, we introduce the notation and present a deterministic
version of materials planning problems. The concept of Payoff Table
is discussed in Section 2. Illustrative algorithms are provided in
Section 3. We describe the graphical user interface developed for
Payoff Table in Section 4. Finally, a complete example is presented
in Section 5.
1. Formulation of the Materials Planning Problem
To formulate the problem defined in the PPPT computation, we
introduce the following notation for a deterministic materials
planning problem.
T, set of periods that comprise the planning horizon.
J, set of products.
J.sub.e .OR right.J, set of end products.
J.sub.a .OR right.J, set of subassemblies.
I, set of components.
I.sub.R .OR right.I, set of out-sourcing components. (Note, I.sub.r
.andgate.J.sub.a =empty and I=I.sub.r .orgate.J.sub.a.)
I.sub.j .OR right.I, set of components in the BOM of product
j.epsilon.J.
d.sub.j,t, demand for end product j.epsilon.J.sub.e in period
t.
c.sub.j, cycle time of product j.epsilon.J.
O.sub.i,j offset for component i in the cycle time of product j
for
i.epsilon.I.sub.j and j.epsilon.J.
.alpha..sub.ij amount of component i that is needed by one unit of
product j for i.epsilon.I.sub.j and j.epsilon.J.
h.sub.i,t, unit holding cost for component i.epsilon.I in period
t.
h.sup.e.sub.j,t, unit holding cost for end product j.epsilon.J, in
period t.
r.sub.j,t, unit penalty for unsatisfied demand of end product
j.epsilon.J.sub.e in period t.
Variables
C.sub.j,t, ending inventory of product j.epsilon.J.sub.e in period
t.
Z.sub.j,t, production volume of end product j.epsilon.J.sub.e in
period t.
L.sub.j,t, unsatisfied demand of end product j.epsilon.J.sub.e in
period t.
Q.sub.i,t, ending inventory of component i.epsilon.I in period
t.
Y.sub.i,t, consumed volume of component i.epsilon.I in period
I.
Z.sub.i,t, production/procurement volume of component i.epsilon.I
in period t.
Note
C.sub.j,0, initial inventory of product j.epsilon.J.sub.e at the
beginning of the planning horizon.
Q.sub.i,0, initial inventory of component i.epsilon.I at the
beginning of the planning horizon.
Production and procurement decisions are made at the beginning of
each period based on the information available at that time.
Demands materialize by the end of each period. Unsatisfied demand
will be backlogged, and inventories will be carried over to the
next period. At the end of the planning horizon, all left over
inventories of components and end products will be savaged.
1.1. Deterministic
A Linear Program can be formulated as follows. ##EQU1##
The LP formulation presented above is a simplified version of a
typical materials planning problem with deterministic demands. In
this formulation, all the decisions are made at the beginning of
the planning horizon. The solution of this problem can be obtained
using an implosion technology-based optimization engine, such as
Supply Capability Engine (SCE). For the sake of simplicity, many
advanced features that can be handled by implosion technology are
omitted in this formulation.
Notice that the production cost and the procurement cost are not
included in this formulation. However, it is easy to show that when
these costs are linear and time-invariant, they do not affect the
solution of the optimization problem. Furthermore, the cost
minimization formulation presented here is equivalent to a profit
maximization formulation since the demand, hence the revenue from
sales, is independent of the production decision. Even in the case
of lost sales, the situation can be handled by including the loss
in sales as a penalty cost of the unsatisfied demand.
The formulation presented here describes a single-scenario problem.
When the demand Uncertainty is modeled via scenarios, the above
formulation can still be used to obtain a solution for each
scenario individually. However, the single-scenario solution may
perform badly when a different scenario actually occurs.
1.2. Scenario-based analysis
Let
S=set of scenarios.
N=number of the scenarios.
D.sup.s =demand under scenario s.epsilon.S.D.sup.s can be expressed
by the matrix ##EQU2## where n is the number of periods in the
planning horizon, m is the number of the products. To simplify the
notation, we suppress the superscript for each element in the
matrix.
P.sup.s =production decision under scenario s.epsilon.S. It is
referred to as the Scenario solution for scenario s.
Note that a scenario solution consists of both a production
schedule for all products and a procurement schedule for all
components in each period of the entire planning horizon. It can be
expressed by the following matrix ##EQU3##
To deal with the demand uncertainty over a period of time, recourse
actions may be taken so that unimplemented decisions can be
modified according to new information when it becomes available.
For example, at t=1, Z.sub.11 is implemented; Z.sub.12, . . . ,
Z.sub.1n are computed but not implemented. There are different
types of recourse actions that can be taken. We will discuss two
possibilities: the simple recourse and the full recourse.
In the simple recourse, production decisions cannot be changed
(even as new information becomes available). In this case, the LP
formulation is similar to that of the single-scenario case.
Nevertheless, the objective function will be the weighted-average
of the objective functions for individual scenarios, and all the
constraints have to be duplicated for each scenario.
The full recourse allows all the production and procurement
decisions to be revisited every time period and adjustments can be
made based on the latest information. With fall recourse,
additional constraints reflecting the nonanticipativity assumption
of a production decision must be added in the model. The definition
of the nonanticipativity is given in the next section.
To obtain an optimal solution of a multi-scenario problem usually
requires solving a stochastic LP program. Especially in the full
recourse case it is far more complex than that for the
single-scenario model. Therefore, a heuristic-based solution like
the payoff table approach becomes necessary.
The payoff table approach is also a useful tool for sensitivity
analysis. We can use the payoff table to find out the expected
performance of a particular production plan under different demand
scenarios.
2. The concept of PPPT
The PPPT is a tool for production planning decision-making based on
scenario analysis and the IBM implosion technology.
The PPPT computation is based on the following key concepts.
Scenarios are used to represent possible realizations of uncertain
demand.
For each demand scenario, a deterministic solution approach (such
as the IBM implosion technology) can be used to produce a
scenario-dependent production plan. It is clear that a production
plan based on a particular demand scenario is optimal only if the
actual demand scenario turns out to be the same scenario used for
the planning.
In reality a different demand scenario may actually occur, and
therefore, the production plan may not be optimal for the actual
demand scenario. To minimize the unfavorable impact of the mismatch
between the production plan and the actual demand scenario, we
would like to evaluate the expected overall performance measure and
the robustness of a production plan against all different demand
scenarios.
Furthermore, when a production plan is evaluated against a
different demand scenario, we need to keep in mind that the
production plan will be re-optimized when new information about
demand becomes available, and only the initial portion of the
production plan has to be fixed and implemented.
Based on the evaluation for each scenario-dependent production
plan, we will be able to choose one based on the expected
performance or the robustness of the production plan against all
possible demand scenarios.
2.1. Scenario Representation for Demand
The tree structure is utilized internally to represent demand
scenarios. A general scenario tree can be illustrated by FIG. 1
(numeral 12).
Each node except the root represents the demands for all products
in a given period. A complete path from the root to an end node
forms a demand scenario. Different demand scenarios may have the
same demands initially and then diverge from a certain point. A
special type of scenario tree is the ones with the canonical
structure. In a canonical tree, the root is the only common node
for any two branches. A canonical demand scenario tree means that
all demand scenarios diverge from the first period in the planning
horizon.
The scenario table is provided by users as an input. It specifies
the demand scenarios over the planning horizon. Suppose there are N
demand scenarios and the number of periods in the planning horizon
is n. A scenario table is an N.times.(n+1) matrix. Each row of the
scenario table describes a demand scenario with the first n
elements representing the demands in the n periods and the last
element being the probability of that the scenario will occur. A
demand for a given scenario in a given period is labeled by an
integer. Usually, the first n elements of Scenario 1 are assigned
to be 1s. For Scenario 2, if the demand in a given period is
different from the that in the same period for Scenario 1, then the
number 2 will be used to represent the demand for Scenario 1; if
the demand is the same with that in the same period for Scenario 1,
the number will remain the same. The same procedure applies for the
rest of the scenarios as well. Notice that demands in different
periods can also be represented by the same integer number. But the
actual demands can be different in different periods. In fact, the
actual demand quantities will be provided as a separate input by
users.
In the following example, we have a problem with 3 different
scenarios. The planning horizon is 2 periods. The scenario table is
given below:
1 1 0.5
1 2 0.3
2 3 0.2
The corresponding scenario tree is shown in FIG. 2 (numeral
14).
2.2. The structure of PPPT
In the PPPT computation, the scenario-based representation for
demand is used. A demand scenario is a multi-period statement of
demand for a group of products. A set of demand scenarios and the
probabilities associated with each scenarios are provided as inputs
to represent the uncertain demand.
For each of the demand scenarios, the PPPT first computes the
optimal production plan under a certain performance criterion. For
a given demand scenario, the optimal production plan specifies the
production quantities for each product in each period with the best
overall performance measure under materials and capacity
constraints. Then the performance measures of the optimal
production plan for the given demand scenario are computed against
all other demand scenarios. A complete payoff table is constructed
by repeating this process for all the demand scenarios. The
structure of a payoff table is illustrated in Table 1.
TABLE 1 ______________________________________ The structure of the
Payoff Table scenario initial plan D.sup.1 D.sup.2 . . . D.sup.N E
.DELTA..sup.+ .DELTA..sup.- ______________________________________
p.sup.1 R.sub.1.1 R.sub.1.2 . . . R.sub.1.N E.sub.1
.DELTA..sub.1.sup.+ .DELTA..sub.1.sup.- p.sup.2 . . . P.sup.N
R.sub.N.1 R.sub.N.2 . . . R.sub.N.N E.sub.N .DELTA..sub.N.sup.+
.DELTA..sub.N.sup.- ______________________________________
The interpretation of the elements in the table is given below.
R.sub.i,i --the optimal payoff for scenario i;
R.sub.i,j --the payoff for scenario j (j.noteq.i) when production
plan P.sup.i (i.epsilon.S) is used for the first period, and then
the production plan is subsequently re-optimized.
E.sub.i --the expected payoff of production plan i at the beginning
of the planning horizon, i.e., ##EQU4## .DELTA..sub.i.sup.+ --the
difference between the maximum payoff and the expected payoff,
and
.DELTA..sub.i.sup.- --the difference between the minimum payoff and
the expected payoff.
3. The computation of PPPT
In general, an optimization problem can be formulated to obtain a
production plan under a certain criterion. Let the objective
function be .function.(P.vertline.D,w) where P is the decision
variable (the production plan), D is the demand which is a random
variable, and w represents all other parameters that affect the
objective function (e.g., costs, supply constraints. etc.). For the
simple recourse case, the optimization problem is given by ##EQU5##
The solution to (1) can be obtained by either an optimization
solver or a heuristic-based approach.
The PPPT is a heuristic approach for solving Problem (1) in a
multi-scenario setting. In the payoff table computation, each
element of the payoff table presents the performance measure
corresponding to a production plan in a particular demand
scenario.
3.1. Diagonal elements
For the computation of diagonal element R.sub.i,j, i=1, . . . ,N,
we have D=D.sup.i. The solution can be obtained by solving the
following problem.
The solution to (2) is called Scenario solution i, which is denoted
by P.sup.i.
3.2. Off-diagonal elements
For the off-diagonal elements, the problem becomes a constrained
optimization problem. In the case of the canonical demand scenario
tree, the general formulation for the computation of off-diagonal
element R.sub.ij, i.noteq.j, can be presented as follows.
where P.sub.1 is the first column of P, and P.sub.1.sup.i is the
first column of P.sup.i. In this case, the assumption made for
computing the off-diagonal elements of the payoff table is that the
initial production plan is made based on demand scenario i but the
actual demand scenario turns out to be j. The decision maker can
adjust the production plan at the beginning of the second period.
However, the production plan made according to scenario i is
already implemented for the first period. Therefore, the decision
variables of the first period have to be fixed in the
re-optimization which is based on the new scenario j.
3.2. 1. Nonanticipativity
One important concept in the implementation of PPPT computation is
the nonanticipativity of the production plan. The nonanticipativity
assumption guarantees that the decisions made in any given period
are implementable, i.e., they do not depend on information that is
not yet available. If a plan is nonanticipative, the decisions made
in a period are identical for any two scenarios that are identical
up to that period. This means that if a node is common to two
different demand scenarios, the decisions must be the same at the
common node for the two production plans made based on the
two demand scenarios. The computation of off-diagonal elements
should respect the nonanticipative assumption in order to make the
production plan implementable- One such example is illustrated in
FIG. 2 (numeral 14), where the nonanticipavity requires that
P.sup.1.sub.1 ==P.sup.2.sub.1. In the case of canonical scenario
trees, the nonanticipativity is implied in the formulation shown in
(3) since the only common node is the root and the re-optimization
always takes place in the second period.
In general, the requirements for the nonanticipative assumption can
be written as follows.
However, the computation of off-diagonal elements when the scenario
tree is non-canonical form is not as straightforward as for
canonical scenario trees. The difficulty is that for every common
node, the nonanticipativity requires the decisions at the node to
be the same for all demand scenarios sharing the node. The solution
respecting such a property, i.e., condition (4), and at the same
time without compromising the optimality would require the use of
stochastic LP technique, which could be computationally complex. To
overcome this difficulty, a heuristic is adapted in the PPPT
computation for the scenario tree with non-canonical form.
3.2.2. The Algorithm for Computing R.sub.ij
Without loss of generality, we assume .rho..sub.1
.gtoreq..rho..sub.2 .gtoreq.. . . .gtoreq..rho..sub.N, where
.rho..sub.j is the probability of scenario j.
Diagonal elements R.sub.i,i is computed the same way as in (2).
For off-diagonal element R.sub.i,j, i.noteq.j, if a node of
scenario j is common to scenario i in period n, let
If a node of scenario j is common to any scenarios other than i,
let i' be the smallest index of all these scenarios. If i'<j,
let
Off-diagonal element R.sub.ij is then obtained by solving (2) with
constraints (5) and (6).
3.3. Upper and Lower Bounds
PPPT also provides the upper and lower bounds of the optimal
solution for the stochastic programming problem with fill recourse.
The upper and lower bounds are given by ##EQU6## respectively.
Proof
Denote the optimal solution by P*. The expected payoff of P* is
given by ##EQU7## where R(P*.vertline.D.sup.j) is the payoff of P*
under scenario i.
Since R.sub.ii .gtoreq.R(P*.vertline.D.sup.i), ##EQU8##
On the other hand, since P* is optimal, its expected payoff is at
least as good as the expected payoff of any scenario solution,
i.e.,
3.4. Optimization Engine
In the PPPT implementation, we preferably use SCE as the
optimization engine. SCE is a production planning optimization
software developed at IBM Research for computing the capability to
supply finished goods based on availability of constrained
components..SCE is based on the implosion technology. It can
perform resource allocation under constraints by using demands,
available resources, and the Bill Of Manufacture (includes BOM as
well as Bill of Capacities) to determine a feasible product mix
which meets the user defined criterion The type of the objective
function used by SCE can be one of the three options: Revenue,
Profit, or Priority. Among them, Priority is not used in the PPPT
computation. Furthermore, since SCE does not include cost
information for inventory holding, backlog penalty, and
obsolescence, the profit obtained by SCE will be adjusted to
reflect these costs. However, these costs are computed after the
SCE optimization is completed.
The diagonal elements of the PPPT are obtained by running SCE for
the given reference scenarios. The off-diagonal elements are
computed by running SCE with the demand given by the new scenario
and the production constraints imposed by the production plan made
based on the reference scenario and the nonanticipative assumption.
For example, for an off-diagonal element which represents the
performance measure under scenarios for the production plan made
initially based on scenario i, we first obtain the production
constraints (5) and (6), then run SCE against the demand scenario
j.
4. The Graphical User Interface
The graphical user interface is built in forms of World Wide Web
(WWW) pages. The programs implementing the PPPT computation are
installed on a server which is also the Web server hosting the WWW
pages for the graphical user interface of PPPT. All the required
data are stored on the same server. A user accesses the graphical
user interface of PPPT by linking a Web browser to the Universal
Resource Locator (URL) of the server. A Logon page will be
presented when the connection is established (See FIGS. 3-8,
numerals 16-26).
The Logon Page (see FIG. 3)
The user is required to enter a valid pair of userid and password.
If the userid and the password entered are not valid, further
access to other PPPT WWW pages will be denied. Otherwise, the Web
browser will connect to the PPPT Main Page.
The Main Page (see FIG. 4)
A Main Task List table will be presented. The four major steps of
the PPPT computation are listed with a brief description for each
step. The current status of each of the four steps is also reported
in the table. The user should choose an activity from the Main Task
List.
set parameters (see FIG. 5): this step allows the user to
view/change the current setting of the following parameters: the
number of demand scenarios, the number of periods in the planning
horizon, the type of optimization engine to be used, and the type
of objective for optimization.
modify data: allows the user to view/modify the data used for the
PPPT computation. There are four types of data files to be
viewed/modified:
Scenario File,
Bill of Materials File,
Supply Volume File, and
Demand Volume Files
The user can choose one of the files for viewing/editing.
compute payoff table: invokes the server programs to perform the
desired PPPT computation. Upon the completion of the PPPT
computation, the message "Pay-off Table computation is completed!"
will be displayed.
view payoff table: allows the user to view the payoff table in
either table format or chart format.
Data Viewing/Editing Pages
For the Bill of Materials file, no editing capability is provided.
For Scenario, Supply Volume, and Demand Volume files, the user can
view and edit the data if desired (see FIG. 6). A complete table
will be presented first for viewing. If editing is allowed, the
user can click on the line number to enter the editing mode. Only
one row will be displayed at a time in the editing mode.
PPPT Display Pages
If the table format is selected, a user may choose one performance
measure to be displayed from the following three choices: Revenue,
Profit, and Serviceability. If Profit is selected, the user may
also provide the backlog penalty factor and the obsolescence factor
as required for the profit computation. The payoff table displayed
in the table form contains the complete payoff table of the
selected performance measure and the weighted average performance
measure for each plan as well as the differences between the
weighted average and the best(worst) performance measure of the
plan against a particular scenario. The plan with the best weighted
average performance measure will be highlighted in the table (see
FIG. 7).
In the bar chart format, a user may choose to display a bar chart
that is corresponding to a row or a column in the payoff table,
i.e., the performance measures of a given plan against different
scenarios or the performance measures of different plans for a
given scenario. The performance measure displayed in the bar chart
form can be either Revenue or Profit or Serviceability. The backlog
penalty factor and the obsolescence factor are required as inputs
when Profit is selected (see FIG. 8).
5. An Example
The invention is now referenced by an illustrative example. For
machine realization of the invention, one may consider the example
parameters in the following Tables II-X to be inputs for operation
thereupon by the method programmed in Perl and effectuated by a CPU
and memory, and Table XI or FIGS. 7, 8 to be illustrative output
displays.
Description
This is a two-period problem with six products and four demand
scenarios.
Data preparation
The data required for the PPPT computation are listed in Tables
2-10.
TABLE 2 ______________________________________ Demand Volume File 1
Part Number Geography Period 1 Period 2
______________________________________ SUP-DT WW 1,865 1,892 MC-DT
WW 12,450 15,040 SUP-NB WW 10,300 8,930 MC-NB WW 6,700 8,500
SUP-SVR WW 7,540 7,990 MC-SVR WW 5,200 6,400
______________________________________
TABLE 3 ______________________________________ Demand Volume File 2
Part Number Geography Period 1 Period 2
______________________________________ SUP-DT WW 17,718 17,974
MC-DT WW 11,828 14,288 SUP-NB WW 12,360 10,716 MC-NB WW 8,040
10,200 SUP-SVR WW 7,540 7,990 MC-SVR WW 5,200 6,400
______________________________________
TABLE 4 ______________________________________ Demand Volume File 3
Part Number Geography Period 1 Period 2
______________________________________ SUP-DT WW 21,448 21,758
MC-DT WW 14,318 17,296 SUP-NB WW 11,845 10,270 MC-NB WW 7,705 9,775
SUP-SVR WW 8,671 9,189 MC-SVR WW 5,980 7,360
______________________________________
TABLE 5 ______________________________________ Demand Volume File 4
Part Number Geography Period 1 Period 2
______________________________________ SUP-DT WW 20,375 2,067 MC-DT
WW 13,602 16,431 SUP-NB WW 14,214 12,323 MC-NB WW 9,246 11,730
SUP-SVR WW 8,671 9,189 MC-SVR WW 5,980 7,360
______________________________________
TABLE 6 ______________________________________ Supply Volume File
Part Number Geography Period 1 Period 2
______________________________________ MEM-4 MB WW 250,000 250,000
______________________________________
TABLE 7 ______________________________________ Bill of Materials
File Parent Part Child Part Number Number Geography Usage Rate
______________________________________ SUP-DT P-486 WW 1 SUP-DT
HD-240 WW 1 SUP-DT MEM-4 MB WW 1 MC-DT P-486 WW 1 MC-DT HD-480 WW 1
MC-DT MEM-4 MB WW 1 SUP-NB P-PENTIUM WW 1 SUP-NB HD-480 WW 1 SUP-NB
MEM-4 MB WW 2 SUP-NB CD-ROM WW 1 MC-NB P-PENTIUM WW 1 MC-NB HD-720
WW 1 MC-NB MEM-4 MB WW 2 MC-NB CD-ROM WW 1 SUP-SVR P-POWERPC WW 1
SUP-SVR HD-720 WW 1 SUP-SVR MEM-4 MB WW 4 SUP-SVR CD-ROM WW 1
SUP-SVR TOK-RING WW 1 MC-SVR P-POWERPC WW 1 MC-SVR HD-720 WW 1
MC-SVR MEM-4 MB WW 4 MC-SVR CD-ROM WW 1 MC-SVR MULT-MED WW 1
______________________________________
TABLE 8 ______________________________________ Scenario File
Scenario Period 1 Period 2 Probability
______________________________________ 1 1 1 0.42 2 2 2 0.18
3 3 3 0.28 4 4 4 0.12 ______________________________________
TABLE 9 ______________________________________ Revenue File Part
Number Geography Revenue ______________________________________
SUP-DT WW 1,000 MC-DT WW 1,100 SUP-NB WW 2,000 MC-NB WW 2,400
SUP-SVR WW 3,500 MC-SVR WW 4,000
______________________________________
TABLE 10 ______________________________________ Profit File Part
Number Geography Profit ______________________________________
SUP-DT WW 250 MC-DT WW 250 SUP-NB WW 500 MC-NB WW 700 SUP-SVR WW
600 MC-SVR WW 1,100 ______________________________________
Procedure
1. Start a Web Browser and link to the URL of the PPPT Web
server.
2. When prompted, enter the userid and password.
3. On the Main Task List page, select "set parameters".
4. On the Set Parameters page, enter "4" for the number of
scenarios, "2" for the number of periods, select "LP Optimization"
for the optimization engine, and "Profit" for the objective type.
Then click the "Submit" button.
5. Go back to the Main Task List page. Select "modify data".
6. Modify the data by following appropriate links as desired.
7. Go back to the Main Task List page. Select "compute payoff
table".
8. Wait until a screen with the message "The Payoff Table
computation is completed".
9. Go to the View Payoff Table Results page, select "view output
tables" to view the payoff table in table format, or select "view
output charts" to view the payoff table in bar-chart format.
10. On the View Output Tables page, select one from "Profit",
"Revenue", and "Serviceability". If "profit" is selected, enter the
values for "Backlog penalty" and "Obsolescence factor". Then click
on "Submit" to view the output.
11. On the View Output charts page, select either "Plan" or
"Scenario" and the number, also select one from "Profit",
"Revenue", and "Serviceability". If "profit" is selected, enter the
values for "Backlog penalty" and "Obsolescence factor". Then click
on "Submit" to view the output.
12. Repeat any step(s) as desired.
Outputs
The results of this example are summarized in Table 11. The revenue
and profit figures are in million dollars.
TABLE 11
__________________________________________________________________________
PPPT Results j scenario 1 2 3 4 Statistics p.sub.j probability 0.42
0.18 0.28 0.12 Mean .DELTA.+ .DELTA.-
__________________________________________________________________________
P.sup.1 revenue 243.5 240.1 243.5 243.5 242.9 1.4 -2.8 profit 41.57
35.77 30.77 26.79 35.73 5.84 -8.94 P.sup.2 revenue 240.3 255.5
251.1 255.1 247.8 7.3 -7.5 profit 35.87 43.66 33.99 32.35 36.32
7.34 -3.97 P.sup.3 revenue 243.5 251.7 280 276.1 259.1 20.9 -16.6
profit 30.89 34.23 47.8 41.14 37.46 10.34 -6.57 P.sup.4 revenue
243.5 255.1 276.3 293.4 260.8 32.6 -17.3 profit 26.99 32.48 41.26
50.21 34.76 15.45 -7.77
__________________________________________________________________________
Backlog penalty factor = 0.2, obsolescence factor = 0.5
In this PPPT, both the revenues and the profits are listed for the
comparison purpose. The highest mean in terms of revenues is
archived by Plan 4, while the highest mean in terms of profits is
archived by Plan 3. Furthermore, if one's objective is to minimize
the variability of the performance under different scenarios, the
best plan will be the one with the smallest .DELTA.+ and .DELTA.-
Plan 1 in this example).
We can also obtain the upper and lower bounds of the optimal
solution from the table.
Revenue
R.sub.U =261.8 million dollars, R.sub.L =260.8 million dollars.
Profit
R.sub.U =44.72 million dollars, R.sub.L =37.46 million dollars.
* * * * *